paper

On cycles in intersection graph of rings

arXiv:1401.6619

Abstract

Let $R$ be a commutative ring with non-zero identity. We describe all $C_{3}$ - and $C_{4}$ -free intersection graph of non-trivial ideals of $R$ as well as $C_{n}$ -free intersection graph when $R$ is a reduced ring. Also, we shall describe all complete, regular and $n$ -claw-free intersection graphs. Finally, we shall prove that almost all Artin rings $R$ have Hamiltonian intersection graphs. We show that such graphs are indeed pancyclic.

8 pages, 6 figures